Question

Prove that opposite sides of parallelogram are equal...​

Answer 1

Answer:

The opposite sides of a parallelogram are equal (and conversely: if the opposite sides of a quadrilateral are equal, it is a parallelogram). ... If one pair of opposite sides of a quadrilateral is equal and parallel, then the quadrilateral is a parallelogram

HOPE IT'S HELPFUL !

Answer 2

To Prove:

opposite sides of parallelogram are equal.

Proof :

Let us consider a parallelogram ABCD in which AB||CD and BC|| AD .

$\sf \: now \: \: \: in \triangle \: ABC \: and \: \triangle CDA \: \\ \angle \: CAB \: = \angle \:ACD \: \: \: \: \: \: ( \sf \: alternate \: angle) \\ \angle \: ACB = \angle \: CAD \: \: \: \: \: \: ( \sf \: alternate \: angle) \\ \:AC = CA \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ( \sf \: common) \\ \therefore \triangle \: ABC \cong \: CDA \: \: \: \: \: \sf(ASA \: congruency) \\ \sf \: \sf \: hence \: \: AB = CD \: and \: BC = AD \: \: \: \: \: \: \: \sf \:( C.PC.T)$